• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.491-502
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• 2016

In this paper, as a generalization of symmetric bi-derivations and symmetric bi-f-derivations of a lattice, we introduce the notion of symmetric bi-(f, g)-derivations of a lattice. Also, we define the isotone symmetric bi-(f, g)-derivation and obtain some interesting results about isotone. Using the notion of $Fix_a(L)$ and KerD, we give some characterization of symmetric bi-(f, g)-derivations in a lattice.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.297-307
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• 2014

The present paper gives the notion of a derivation on a CI-algebra X and investigates related properties. We define a set $Fix_d(X)$ by $Fix_d(X)=\{x{\in}X{\mid}d(x)=x\}$, where d is a derivation on a CI-algebra X. We show that $Fix_d(X)$ is a subalgebra of X. Also, we prove some one-to-one and onto derivation theorems. Moreover, we study a regular derivation on a CI-algebra and an isotone derivation on a transitive CI-algebra.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.643-649
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• 2014

In this paper, we introduce the concept of a (f, g)-derivation which is a generalization of f-derivation in an incline algebra and give some properties of incline algebras. Also, we consider the kerd and k-ideal with respect to (f, g)-derivation in an incline algebra.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.2
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• pp.125-136
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• 2022

The goal of this paper is to introduce the notion of generalized symmetric bi-f-derivations in lattices and to study some properties of generalized symmetric f-derivations of lattice. Moreover, we consider generalized isotone symmetric bi-f-derivations and fixed sets related to generalized symmetric bi-f-derivations.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.683-690
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• 2013

In this paper, we introduce the concept of a right derivation in incline algebras and give some properties of incline algebras. Also, the concept of d-ideal is introduced in an incline algebra with respect to right derivation.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.37-48
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• 2016

The aim of this paper is to introduce the notion of a generalized derivations of BCH-algebras and some related properties are investigated.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1119-1131
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• 2019

In this paper, we introduce the notion of generalized f-derivation of lattice implication algebra and investigate some related properties. Also, we prove that if D is a generalized f-derivation associated with an f-derivation d of L, then D(x → y) = f(x) → D(y) for all x, y ∈ L.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.127-138
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• 2015

In this paper, we introduce the notion of f-derivation in a BE-algebra, and consider the properties of f-derivations. Also, we characterize the fixed set $Fix_d(X)$ and Kerd by f-derivations. Moreover, we prove that if d is a f-derivation of a BE-algebra, every f-filter F is a a d-invariant.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.441-451
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• 2019

In this paper, we introduce the notion of symmetric bi-f-derivation on subtraction algebra and investigated some related properties. Also, we prove that if D : X → X is a symmetric bi-f-derivation on X, then D satisfies D(x - y, z) = D(x, z) - f(y) for all x, y, z ∈ X.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.387-393
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• 2021

In this paper, we introduce the notion of symmetric bi-derivations on subtraction algebra and investigated some related properties. We prove that a map D : X × X → X is a symmetric bi-derivation on X if and only if D is a symmetric map and it satisfies D(x - y, z) = D(x, z) - y for all x, y, z ∈ X.